Answer
$\theta=2^{\circ}$
Work Step by Step
1. Tangent and cotangent are reciprocals
$\tan\theta=\frac{1}{\cot 5\theta}$
2. Rewrite cotangent as a tengent
$\tan(3\theta -4^{\circ})=\tan(5\theta-8^{\circ})$
3.Since the tangent values are equal, the angles themselves must be equal.
$5\theta -3\theta= -4+8$
$2\theta=4$
$\theta=2^{\circ}$
